Properties

Label 4015.2.a.h.1.2
Level 4015
Weight 2
Character 4015.1
Self dual Yes
Analytic conductor 32.060
Analytic rank 0
Dimension 37
CM No

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Newspace parameters

Level: \( N \) = \( 4015 = 5 \cdot 11 \cdot 73 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0599364115\)
Analytic rank: \(0\)
Dimension: \(37\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) = 4015.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.58511 q^{2}\) \(-0.179292 q^{3}\) \(+4.68277 q^{4}\) \(+1.00000 q^{5}\) \(+0.463488 q^{6}\) \(+2.09214 q^{7}\) \(-6.93525 q^{8}\) \(-2.96785 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.58511 q^{2}\) \(-0.179292 q^{3}\) \(+4.68277 q^{4}\) \(+1.00000 q^{5}\) \(+0.463488 q^{6}\) \(+2.09214 q^{7}\) \(-6.93525 q^{8}\) \(-2.96785 q^{9}\) \(-2.58511 q^{10}\) \(+1.00000 q^{11}\) \(-0.839582 q^{12}\) \(-4.99735 q^{13}\) \(-5.40839 q^{14}\) \(-0.179292 q^{15}\) \(+8.56281 q^{16}\) \(+6.36330 q^{17}\) \(+7.67222 q^{18}\) \(-4.13266 q^{19}\) \(+4.68277 q^{20}\) \(-0.375103 q^{21}\) \(-2.58511 q^{22}\) \(-6.06585 q^{23}\) \(+1.24343 q^{24}\) \(+1.00000 q^{25}\) \(+12.9187 q^{26}\) \(+1.06999 q^{27}\) \(+9.79700 q^{28}\) \(-8.53637 q^{29}\) \(+0.463488 q^{30}\) \(+0.350326 q^{31}\) \(-8.26527 q^{32}\) \(-0.179292 q^{33}\) \(-16.4498 q^{34}\) \(+2.09214 q^{35}\) \(-13.8978 q^{36}\) \(+0.503875 q^{37}\) \(+10.6834 q^{38}\) \(+0.895983 q^{39}\) \(-6.93525 q^{40}\) \(+11.4873 q^{41}\) \(+0.969681 q^{42}\) \(-3.35980 q^{43}\) \(+4.68277 q^{44}\) \(-2.96785 q^{45}\) \(+15.6809 q^{46}\) \(-10.9259 q^{47}\) \(-1.53524 q^{48}\) \(-2.62296 q^{49}\) \(-2.58511 q^{50}\) \(-1.14089 q^{51}\) \(-23.4014 q^{52}\) \(-6.15103 q^{53}\) \(-2.76603 q^{54}\) \(+1.00000 q^{55}\) \(-14.5095 q^{56}\) \(+0.740953 q^{57}\) \(+22.0674 q^{58}\) \(+10.9021 q^{59}\) \(-0.839582 q^{60}\) \(+12.5067 q^{61}\) \(-0.905630 q^{62}\) \(-6.20916 q^{63}\) \(+4.24098 q^{64}\) \(-4.99735 q^{65}\) \(+0.463488 q^{66}\) \(+0.730531 q^{67}\) \(+29.7979 q^{68}\) \(+1.08756 q^{69}\) \(-5.40839 q^{70}\) \(+9.27558 q^{71}\) \(+20.5828 q^{72}\) \(+1.00000 q^{73}\) \(-1.30257 q^{74}\) \(-0.179292 q^{75}\) \(-19.3523 q^{76}\) \(+2.09214 q^{77}\) \(-2.31621 q^{78}\) \(+13.0212 q^{79}\) \(+8.56281 q^{80}\) \(+8.71172 q^{81}\) \(-29.6958 q^{82}\) \(-2.88990 q^{83}\) \(-1.75652 q^{84}\) \(+6.36330 q^{85}\) \(+8.68544 q^{86}\) \(+1.53050 q^{87}\) \(-6.93525 q^{88}\) \(+12.2092 q^{89}\) \(+7.67222 q^{90}\) \(-10.4551 q^{91}\) \(-28.4050 q^{92}\) \(-0.0628105 q^{93}\) \(+28.2447 q^{94}\) \(-4.13266 q^{95}\) \(+1.48189 q^{96}\) \(+2.56372 q^{97}\) \(+6.78064 q^{98}\) \(-2.96785 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(37q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut +\mathstrut 37q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 50q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(37q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut +\mathstrut 37q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 50q^{9} \) \(\mathstrut +\mathstrut 5q^{10} \) \(\mathstrut +\mathstrut 37q^{11} \) \(\mathstrut +\mathstrut 6q^{12} \) \(\mathstrut +\mathstrut 11q^{13} \) \(\mathstrut +\mathstrut 11q^{14} \) \(\mathstrut +\mathstrut 3q^{15} \) \(\mathstrut +\mathstrut 43q^{16} \) \(\mathstrut +\mathstrut 38q^{17} \) \(\mathstrut +\mathstrut 11q^{18} \) \(\mathstrut +\mathstrut 34q^{19} \) \(\mathstrut +\mathstrut 43q^{20} \) \(\mathstrut +\mathstrut 39q^{21} \) \(\mathstrut +\mathstrut 5q^{22} \) \(\mathstrut +\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut 25q^{24} \) \(\mathstrut +\mathstrut 37q^{25} \) \(\mathstrut -\mathstrut 9q^{26} \) \(\mathstrut +\mathstrut 3q^{27} \) \(\mathstrut +\mathstrut 14q^{28} \) \(\mathstrut +\mathstrut 58q^{29} \) \(\mathstrut +\mathstrut 9q^{30} \) \(\mathstrut +\mathstrut 8q^{31} \) \(\mathstrut +\mathstrut 14q^{32} \) \(\mathstrut +\mathstrut 3q^{33} \) \(\mathstrut +\mathstrut 8q^{34} \) \(\mathstrut +\mathstrut 6q^{35} \) \(\mathstrut +\mathstrut 20q^{36} \) \(\mathstrut +\mathstrut 2q^{37} \) \(\mathstrut +\mathstrut 15q^{38} \) \(\mathstrut +\mathstrut 14q^{39} \) \(\mathstrut +\mathstrut 12q^{40} \) \(\mathstrut +\mathstrut 62q^{41} \) \(\mathstrut -\mathstrut 13q^{42} \) \(\mathstrut +\mathstrut 30q^{43} \) \(\mathstrut +\mathstrut 43q^{44} \) \(\mathstrut +\mathstrut 50q^{45} \) \(\mathstrut +\mathstrut 31q^{46} \) \(\mathstrut +\mathstrut 5q^{47} \) \(\mathstrut -\mathstrut 25q^{48} \) \(\mathstrut +\mathstrut 59q^{49} \) \(\mathstrut +\mathstrut 5q^{50} \) \(\mathstrut +\mathstrut 23q^{51} \) \(\mathstrut -\mathstrut q^{52} \) \(\mathstrut +\mathstrut 18q^{53} \) \(\mathstrut +\mathstrut 13q^{54} \) \(\mathstrut +\mathstrut 37q^{55} \) \(\mathstrut +\mathstrut 22q^{56} \) \(\mathstrut +\mathstrut 5q^{57} \) \(\mathstrut -\mathstrut 40q^{58} \) \(\mathstrut +\mathstrut 15q^{59} \) \(\mathstrut +\mathstrut 6q^{60} \) \(\mathstrut +\mathstrut 57q^{61} \) \(\mathstrut +\mathstrut 20q^{62} \) \(\mathstrut -\mathstrut 29q^{63} \) \(\mathstrut +\mathstrut 10q^{64} \) \(\mathstrut +\mathstrut 11q^{65} \) \(\mathstrut +\mathstrut 9q^{66} \) \(\mathstrut -\mathstrut 14q^{67} \) \(\mathstrut +\mathstrut 53q^{68} \) \(\mathstrut +\mathstrut 24q^{69} \) \(\mathstrut +\mathstrut 11q^{70} \) \(\mathstrut +\mathstrut 8q^{71} \) \(\mathstrut +\mathstrut 15q^{72} \) \(\mathstrut +\mathstrut 37q^{73} \) \(\mathstrut +\mathstrut 7q^{74} \) \(\mathstrut +\mathstrut 3q^{75} \) \(\mathstrut +\mathstrut 59q^{76} \) \(\mathstrut +\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut q^{78} \) \(\mathstrut +\mathstrut 42q^{79} \) \(\mathstrut +\mathstrut 43q^{80} \) \(\mathstrut +\mathstrut 61q^{81} \) \(\mathstrut -\mathstrut 22q^{82} \) \(\mathstrut +\mathstrut 44q^{83} \) \(\mathstrut +\mathstrut 66q^{84} \) \(\mathstrut +\mathstrut 38q^{85} \) \(\mathstrut -\mathstrut q^{86} \) \(\mathstrut -\mathstrut 26q^{87} \) \(\mathstrut +\mathstrut 12q^{88} \) \(\mathstrut +\mathstrut 69q^{89} \) \(\mathstrut +\mathstrut 11q^{90} \) \(\mathstrut -\mathstrut 10q^{91} \) \(\mathstrut -\mathstrut 21q^{92} \) \(\mathstrut -\mathstrut 26q^{93} \) \(\mathstrut +\mathstrut 29q^{94} \) \(\mathstrut +\mathstrut 34q^{95} \) \(\mathstrut -\mathstrut 9q^{96} \) \(\mathstrut +\mathstrut 37q^{97} \) \(\mathstrut -\mathstrut 15q^{98} \) \(\mathstrut +\mathstrut 50q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.58511 −1.82795 −0.913973 0.405775i \(-0.867002\pi\)
−0.913973 + 0.405775i \(0.867002\pi\)
\(3\) −0.179292 −0.103514 −0.0517571 0.998660i \(-0.516482\pi\)
−0.0517571 + 0.998660i \(0.516482\pi\)
\(4\) 4.68277 2.34139
\(5\) 1.00000 0.447214
\(6\) 0.463488 0.189218
\(7\) 2.09214 0.790753 0.395377 0.918519i \(-0.370614\pi\)
0.395377 + 0.918519i \(0.370614\pi\)
\(8\) −6.93525 −2.45198
\(9\) −2.96785 −0.989285
\(10\) −2.58511 −0.817482
\(11\) 1.00000 0.301511
\(12\) −0.839582 −0.242367
\(13\) −4.99735 −1.38602 −0.693008 0.720930i \(-0.743715\pi\)
−0.693008 + 0.720930i \(0.743715\pi\)
\(14\) −5.40839 −1.44545
\(15\) −0.179292 −0.0462929
\(16\) 8.56281 2.14070
\(17\) 6.36330 1.54333 0.771663 0.636032i \(-0.219425\pi\)
0.771663 + 0.636032i \(0.219425\pi\)
\(18\) 7.67222 1.80836
\(19\) −4.13266 −0.948098 −0.474049 0.880498i \(-0.657208\pi\)
−0.474049 + 0.880498i \(0.657208\pi\)
\(20\) 4.68277 1.04710
\(21\) −0.375103 −0.0818542
\(22\) −2.58511 −0.551146
\(23\) −6.06585 −1.26482 −0.632408 0.774635i \(-0.717933\pi\)
−0.632408 + 0.774635i \(0.717933\pi\)
\(24\) 1.24343 0.253815
\(25\) 1.00000 0.200000
\(26\) 12.9187 2.53356
\(27\) 1.06999 0.205919
\(28\) 9.79700 1.85146
\(29\) −8.53637 −1.58516 −0.792582 0.609765i \(-0.791264\pi\)
−0.792582 + 0.609765i \(0.791264\pi\)
\(30\) 0.463488 0.0846210
\(31\) 0.350326 0.0629204 0.0314602 0.999505i \(-0.489984\pi\)
0.0314602 + 0.999505i \(0.489984\pi\)
\(32\) −8.26527 −1.46111
\(33\) −0.179292 −0.0312107
\(34\) −16.4498 −2.82112
\(35\) 2.09214 0.353636
\(36\) −13.8978 −2.31630
\(37\) 0.503875 0.0828365 0.0414182 0.999142i \(-0.486812\pi\)
0.0414182 + 0.999142i \(0.486812\pi\)
\(38\) 10.6834 1.73307
\(39\) 0.895983 0.143472
\(40\) −6.93525 −1.09656
\(41\) 11.4873 1.79401 0.897006 0.442019i \(-0.145737\pi\)
0.897006 + 0.442019i \(0.145737\pi\)
\(42\) 0.969681 0.149625
\(43\) −3.35980 −0.512365 −0.256182 0.966628i \(-0.582465\pi\)
−0.256182 + 0.966628i \(0.582465\pi\)
\(44\) 4.68277 0.705954
\(45\) −2.96785 −0.442422
\(46\) 15.6809 2.31202
\(47\) −10.9259 −1.59371 −0.796854 0.604171i \(-0.793504\pi\)
−0.796854 + 0.604171i \(0.793504\pi\)
\(48\) −1.53524 −0.221593
\(49\) −2.62296 −0.374709
\(50\) −2.58511 −0.365589
\(51\) −1.14089 −0.159756
\(52\) −23.4014 −3.24520
\(53\) −6.15103 −0.844909 −0.422454 0.906384i \(-0.638831\pi\)
−0.422454 + 0.906384i \(0.638831\pi\)
\(54\) −2.76603 −0.376409
\(55\) 1.00000 0.134840
\(56\) −14.5095 −1.93891
\(57\) 0.740953 0.0981416
\(58\) 22.0674 2.89759
\(59\) 10.9021 1.41933 0.709666 0.704538i \(-0.248846\pi\)
0.709666 + 0.704538i \(0.248846\pi\)
\(60\) −0.839582 −0.108390
\(61\) 12.5067 1.60132 0.800658 0.599122i \(-0.204483\pi\)
0.800658 + 0.599122i \(0.204483\pi\)
\(62\) −0.905630 −0.115015
\(63\) −6.20916 −0.782280
\(64\) 4.24098 0.530122
\(65\) −4.99735 −0.619845
\(66\) 0.463488 0.0570514
\(67\) 0.730531 0.0892486 0.0446243 0.999004i \(-0.485791\pi\)
0.0446243 + 0.999004i \(0.485791\pi\)
\(68\) 29.7979 3.61352
\(69\) 1.08756 0.130926
\(70\) −5.40839 −0.646427
\(71\) 9.27558 1.10081 0.550404 0.834898i \(-0.314474\pi\)
0.550404 + 0.834898i \(0.314474\pi\)
\(72\) 20.5828 2.42571
\(73\) 1.00000 0.117041
\(74\) −1.30257 −0.151421
\(75\) −0.179292 −0.0207028
\(76\) −19.3523 −2.21986
\(77\) 2.09214 0.238421
\(78\) −2.31621 −0.262259
\(79\) 13.0212 1.46499 0.732497 0.680770i \(-0.238355\pi\)
0.732497 + 0.680770i \(0.238355\pi\)
\(80\) 8.56281 0.957351
\(81\) 8.71172 0.967969
\(82\) −29.6958 −3.27936
\(83\) −2.88990 −0.317208 −0.158604 0.987342i \(-0.550699\pi\)
−0.158604 + 0.987342i \(0.550699\pi\)
\(84\) −1.75652 −0.191652
\(85\) 6.36330 0.690196
\(86\) 8.68544 0.936575
\(87\) 1.53050 0.164087
\(88\) −6.93525 −0.739300
\(89\) 12.2092 1.29418 0.647088 0.762416i \(-0.275987\pi\)
0.647088 + 0.762416i \(0.275987\pi\)
\(90\) 7.67222 0.808723
\(91\) −10.4551 −1.09600
\(92\) −28.4050 −2.96142
\(93\) −0.0628105 −0.00651315
\(94\) 28.2447 2.91321
\(95\) −4.13266 −0.424002
\(96\) 1.48189 0.151245
\(97\) 2.56372 0.260306 0.130153 0.991494i \(-0.458453\pi\)
0.130153 + 0.991494i \(0.458453\pi\)
\(98\) 6.78064 0.684948
\(99\) −2.96785 −0.298281
\(100\) 4.68277 0.468277
\(101\) 18.8240 1.87306 0.936529 0.350589i \(-0.114019\pi\)
0.936529 + 0.350589i \(0.114019\pi\)
\(102\) 2.94931 0.292025
\(103\) −5.37508 −0.529622 −0.264811 0.964300i \(-0.585310\pi\)
−0.264811 + 0.964300i \(0.585310\pi\)
\(104\) 34.6579 3.39848
\(105\) −0.375103 −0.0366063
\(106\) 15.9011 1.54445
\(107\) 11.0181 1.06516 0.532582 0.846378i \(-0.321222\pi\)
0.532582 + 0.846378i \(0.321222\pi\)
\(108\) 5.01051 0.482136
\(109\) −6.05401 −0.579869 −0.289934 0.957047i \(-0.593633\pi\)
−0.289934 + 0.957047i \(0.593633\pi\)
\(110\) −2.58511 −0.246480
\(111\) −0.0903406 −0.00857475
\(112\) 17.9146 1.69277
\(113\) 13.4676 1.26692 0.633461 0.773774i \(-0.281634\pi\)
0.633461 + 0.773774i \(0.281634\pi\)
\(114\) −1.91544 −0.179397
\(115\) −6.06585 −0.565643
\(116\) −39.9739 −3.71148
\(117\) 14.8314 1.37116
\(118\) −28.1831 −2.59446
\(119\) 13.3129 1.22039
\(120\) 1.24343 0.113509
\(121\) 1.00000 0.0909091
\(122\) −32.3311 −2.92712
\(123\) −2.05957 −0.185706
\(124\) 1.64050 0.147321
\(125\) 1.00000 0.0894427
\(126\) 16.0513 1.42997
\(127\) −0.00610286 −0.000541541 0 −0.000270771 1.00000i \(-0.500086\pi\)
−0.000270771 1.00000i \(0.500086\pi\)
\(128\) 5.56716 0.492072
\(129\) 0.602384 0.0530370
\(130\) 12.9187 1.13304
\(131\) 17.0010 1.48538 0.742691 0.669634i \(-0.233549\pi\)
0.742691 + 0.669634i \(0.233549\pi\)
\(132\) −0.839582 −0.0730763
\(133\) −8.64610 −0.749712
\(134\) −1.88850 −0.163142
\(135\) 1.06999 0.0920898
\(136\) −44.1310 −3.78421
\(137\) −3.05839 −0.261296 −0.130648 0.991429i \(-0.541706\pi\)
−0.130648 + 0.991429i \(0.541706\pi\)
\(138\) −2.81145 −0.239326
\(139\) 12.9025 1.09438 0.547190 0.837008i \(-0.315698\pi\)
0.547190 + 0.837008i \(0.315698\pi\)
\(140\) 9.79700 0.827998
\(141\) 1.95893 0.164971
\(142\) −23.9784 −2.01222
\(143\) −4.99735 −0.417899
\(144\) −25.4132 −2.11776
\(145\) −8.53637 −0.708907
\(146\) −2.58511 −0.213945
\(147\) 0.470276 0.0387877
\(148\) 2.35953 0.193952
\(149\) −17.9085 −1.46712 −0.733562 0.679623i \(-0.762143\pi\)
−0.733562 + 0.679623i \(0.762143\pi\)
\(150\) 0.463488 0.0378436
\(151\) −0.140306 −0.0114179 −0.00570897 0.999984i \(-0.501817\pi\)
−0.00570897 + 0.999984i \(0.501817\pi\)
\(152\) 28.6611 2.32472
\(153\) −18.8853 −1.52679
\(154\) −5.40839 −0.435821
\(155\) 0.350326 0.0281389
\(156\) 4.19569 0.335924
\(157\) −11.6156 −0.927030 −0.463515 0.886089i \(-0.653412\pi\)
−0.463515 + 0.886089i \(0.653412\pi\)
\(158\) −33.6611 −2.67793
\(159\) 1.10283 0.0874600
\(160\) −8.26527 −0.653427
\(161\) −12.6906 −1.00016
\(162\) −22.5207 −1.76940
\(163\) 9.50264 0.744304 0.372152 0.928172i \(-0.378620\pi\)
0.372152 + 0.928172i \(0.378620\pi\)
\(164\) 53.7923 4.20047
\(165\) −0.179292 −0.0139578
\(166\) 7.47071 0.579840
\(167\) −7.27332 −0.562826 −0.281413 0.959587i \(-0.590803\pi\)
−0.281413 + 0.959587i \(0.590803\pi\)
\(168\) 2.60143 0.200705
\(169\) 11.9735 0.921038
\(170\) −16.4498 −1.26164
\(171\) 12.2651 0.937939
\(172\) −15.7332 −1.19964
\(173\) 14.1344 1.07462 0.537309 0.843386i \(-0.319441\pi\)
0.537309 + 0.843386i \(0.319441\pi\)
\(174\) −3.95651 −0.299942
\(175\) 2.09214 0.158151
\(176\) 8.56281 0.645446
\(177\) −1.95466 −0.146921
\(178\) −31.5621 −2.36568
\(179\) 18.6613 1.39481 0.697404 0.716678i \(-0.254338\pi\)
0.697404 + 0.716678i \(0.254338\pi\)
\(180\) −13.8978 −1.03588
\(181\) −20.3374 −1.51166 −0.755832 0.654765i \(-0.772767\pi\)
−0.755832 + 0.654765i \(0.772767\pi\)
\(182\) 27.0276 2.00342
\(183\) −2.24234 −0.165759
\(184\) 42.0682 3.10131
\(185\) 0.503875 0.0370456
\(186\) 0.162372 0.0119057
\(187\) 6.36330 0.465330
\(188\) −51.1636 −3.73149
\(189\) 2.23856 0.162831
\(190\) 10.6834 0.775053
\(191\) 6.61643 0.478748 0.239374 0.970927i \(-0.423058\pi\)
0.239374 + 0.970927i \(0.423058\pi\)
\(192\) −0.760372 −0.0548751
\(193\) 5.22653 0.376214 0.188107 0.982149i \(-0.439765\pi\)
0.188107 + 0.982149i \(0.439765\pi\)
\(194\) −6.62749 −0.475826
\(195\) 0.895983 0.0641627
\(196\) −12.2827 −0.877339
\(197\) −1.70479 −0.121462 −0.0607308 0.998154i \(-0.519343\pi\)
−0.0607308 + 0.998154i \(0.519343\pi\)
\(198\) 7.67222 0.545241
\(199\) −22.5770 −1.60044 −0.800220 0.599706i \(-0.795284\pi\)
−0.800220 + 0.599706i \(0.795284\pi\)
\(200\) −6.93525 −0.490396
\(201\) −0.130978 −0.00923849
\(202\) −48.6621 −3.42385
\(203\) −17.8593 −1.25347
\(204\) −5.34251 −0.374051
\(205\) 11.4873 0.802306
\(206\) 13.8952 0.968121
\(207\) 18.0026 1.25126
\(208\) −42.7913 −2.96705
\(209\) −4.13266 −0.285862
\(210\) 0.969681 0.0669143
\(211\) 7.96175 0.548110 0.274055 0.961714i \(-0.411635\pi\)
0.274055 + 0.961714i \(0.411635\pi\)
\(212\) −28.8039 −1.97826
\(213\) −1.66303 −0.113949
\(214\) −28.4831 −1.94706
\(215\) −3.35980 −0.229136
\(216\) −7.42063 −0.504910
\(217\) 0.732930 0.0497545
\(218\) 15.6502 1.05997
\(219\) −0.179292 −0.0121154
\(220\) 4.68277 0.315712
\(221\) −31.7996 −2.13907
\(222\) 0.233540 0.0156742
\(223\) −9.86209 −0.660414 −0.330207 0.943908i \(-0.607119\pi\)
−0.330207 + 0.943908i \(0.607119\pi\)
\(224\) −17.2921 −1.15538
\(225\) −2.96785 −0.197857
\(226\) −34.8151 −2.31587
\(227\) 11.1074 0.737227 0.368613 0.929583i \(-0.379833\pi\)
0.368613 + 0.929583i \(0.379833\pi\)
\(228\) 3.46971 0.229787
\(229\) −11.4937 −0.759524 −0.379762 0.925084i \(-0.623994\pi\)
−0.379762 + 0.925084i \(0.623994\pi\)
\(230\) 15.6809 1.03397
\(231\) −0.375103 −0.0246800
\(232\) 59.2019 3.88679
\(233\) 5.63328 0.369048 0.184524 0.982828i \(-0.440926\pi\)
0.184524 + 0.982828i \(0.440926\pi\)
\(234\) −38.3407 −2.50641
\(235\) −10.9259 −0.712728
\(236\) 51.0520 3.32320
\(237\) −2.33459 −0.151648
\(238\) −34.4152 −2.23081
\(239\) −2.26256 −0.146353 −0.0731766 0.997319i \(-0.523314\pi\)
−0.0731766 + 0.997319i \(0.523314\pi\)
\(240\) −1.53524 −0.0990994
\(241\) −1.52060 −0.0979504 −0.0489752 0.998800i \(-0.515596\pi\)
−0.0489752 + 0.998800i \(0.515596\pi\)
\(242\) −2.58511 −0.166177
\(243\) −4.77190 −0.306118
\(244\) 58.5659 3.74930
\(245\) −2.62296 −0.167575
\(246\) 5.32422 0.339460
\(247\) 20.6524 1.31408
\(248\) −2.42960 −0.154280
\(249\) 0.518136 0.0328355
\(250\) −2.58511 −0.163496
\(251\) −17.7964 −1.12330 −0.561648 0.827376i \(-0.689833\pi\)
−0.561648 + 0.827376i \(0.689833\pi\)
\(252\) −29.0761 −1.83162
\(253\) −6.06585 −0.381357
\(254\) 0.0157765 0.000989908 0
\(255\) −1.14089 −0.0714451
\(256\) −22.8737 −1.42960
\(257\) 12.0147 0.749459 0.374729 0.927134i \(-0.377736\pi\)
0.374729 + 0.927134i \(0.377736\pi\)
\(258\) −1.55723 −0.0969487
\(259\) 1.05417 0.0655032
\(260\) −23.4014 −1.45130
\(261\) 25.3347 1.56818
\(262\) −43.9493 −2.71520
\(263\) 10.4883 0.646735 0.323367 0.946274i \(-0.395185\pi\)
0.323367 + 0.946274i \(0.395185\pi\)
\(264\) 1.24343 0.0765280
\(265\) −6.15103 −0.377855
\(266\) 22.3511 1.37043
\(267\) −2.18901 −0.133965
\(268\) 3.42091 0.208965
\(269\) 5.80278 0.353802 0.176901 0.984229i \(-0.443393\pi\)
0.176901 + 0.984229i \(0.443393\pi\)
\(270\) −2.76603 −0.168335
\(271\) −13.2023 −0.801980 −0.400990 0.916082i \(-0.631334\pi\)
−0.400990 + 0.916082i \(0.631334\pi\)
\(272\) 54.4877 3.30380
\(273\) 1.87452 0.113451
\(274\) 7.90626 0.477634
\(275\) 1.00000 0.0603023
\(276\) 5.09278 0.306549
\(277\) −27.7143 −1.66519 −0.832595 0.553882i \(-0.813146\pi\)
−0.832595 + 0.553882i \(0.813146\pi\)
\(278\) −33.3545 −2.00047
\(279\) −1.03972 −0.0622462
\(280\) −14.5095 −0.867108
\(281\) 26.3737 1.57333 0.786663 0.617383i \(-0.211807\pi\)
0.786663 + 0.617383i \(0.211807\pi\)
\(282\) −5.06403 −0.301559
\(283\) −3.57311 −0.212399 −0.106200 0.994345i \(-0.533868\pi\)
−0.106200 + 0.994345i \(0.533868\pi\)
\(284\) 43.4354 2.57742
\(285\) 0.740953 0.0438902
\(286\) 12.9187 0.763897
\(287\) 24.0330 1.41862
\(288\) 24.5301 1.44545
\(289\) 23.4915 1.38185
\(290\) 22.0674 1.29584
\(291\) −0.459654 −0.0269454
\(292\) 4.68277 0.274039
\(293\) 5.34700 0.312375 0.156187 0.987727i \(-0.450080\pi\)
0.156187 + 0.987727i \(0.450080\pi\)
\(294\) −1.21571 −0.0709018
\(295\) 10.9021 0.634745
\(296\) −3.49450 −0.203114
\(297\) 1.06999 0.0620869
\(298\) 46.2954 2.68182
\(299\) 30.3132 1.75305
\(300\) −0.839582 −0.0484733
\(301\) −7.02916 −0.405154
\(302\) 0.362706 0.0208714
\(303\) −3.37499 −0.193888
\(304\) −35.3872 −2.02960
\(305\) 12.5067 0.716130
\(306\) 48.8206 2.79089
\(307\) 3.47864 0.198537 0.0992683 0.995061i \(-0.468350\pi\)
0.0992683 + 0.995061i \(0.468350\pi\)
\(308\) 9.79700 0.558236
\(309\) 0.963708 0.0548234
\(310\) −0.905630 −0.0514363
\(311\) 15.9762 0.905928 0.452964 0.891529i \(-0.350367\pi\)
0.452964 + 0.891529i \(0.350367\pi\)
\(312\) −6.21387 −0.351791
\(313\) 26.1388 1.47746 0.738728 0.674004i \(-0.235427\pi\)
0.738728 + 0.674004i \(0.235427\pi\)
\(314\) 30.0277 1.69456
\(315\) −6.20916 −0.349846
\(316\) 60.9751 3.43012
\(317\) 8.07302 0.453426 0.226713 0.973962i \(-0.427202\pi\)
0.226713 + 0.973962i \(0.427202\pi\)
\(318\) −2.85093 −0.159872
\(319\) −8.53637 −0.477945
\(320\) 4.24098 0.237078
\(321\) −1.97546 −0.110260
\(322\) 32.8065 1.82823
\(323\) −26.2974 −1.46322
\(324\) 40.7950 2.26639
\(325\) −4.99735 −0.277203
\(326\) −24.5653 −1.36055
\(327\) 1.08543 0.0600246
\(328\) −79.6672 −4.39888
\(329\) −22.8585 −1.26023
\(330\) 0.463488 0.0255142
\(331\) −27.5545 −1.51453 −0.757266 0.653106i \(-0.773466\pi\)
−0.757266 + 0.653106i \(0.773466\pi\)
\(332\) −13.5328 −0.742707
\(333\) −1.49543 −0.0819489
\(334\) 18.8023 1.02882
\(335\) 0.730531 0.0399132
\(336\) −3.21193 −0.175225
\(337\) 16.4754 0.897473 0.448736 0.893664i \(-0.351874\pi\)
0.448736 + 0.893664i \(0.351874\pi\)
\(338\) −30.9527 −1.68361
\(339\) −2.41462 −0.131144
\(340\) 29.7979 1.61602
\(341\) 0.350326 0.0189712
\(342\) −31.7067 −1.71450
\(343\) −20.1326 −1.08706
\(344\) 23.3010 1.25631
\(345\) 1.08756 0.0585521
\(346\) −36.5389 −1.96434
\(347\) 12.5370 0.673022 0.336511 0.941680i \(-0.390753\pi\)
0.336511 + 0.941680i \(0.390753\pi\)
\(348\) 7.16699 0.384191
\(349\) −8.88010 −0.475341 −0.237670 0.971346i \(-0.576384\pi\)
−0.237670 + 0.971346i \(0.576384\pi\)
\(350\) −5.40839 −0.289091
\(351\) −5.34710 −0.285407
\(352\) −8.26527 −0.440540
\(353\) −7.50649 −0.399530 −0.199765 0.979844i \(-0.564018\pi\)
−0.199765 + 0.979844i \(0.564018\pi\)
\(354\) 5.05299 0.268564
\(355\) 9.27558 0.492297
\(356\) 57.1730 3.03016
\(357\) −2.38689 −0.126328
\(358\) −48.2414 −2.54964
\(359\) 31.9973 1.68875 0.844377 0.535749i \(-0.179971\pi\)
0.844377 + 0.535749i \(0.179971\pi\)
\(360\) 20.5828 1.08481
\(361\) −1.92109 −0.101110
\(362\) 52.5742 2.76324
\(363\) −0.179292 −0.00941038
\(364\) −48.9590 −2.56615
\(365\) 1.00000 0.0523424
\(366\) 5.79670 0.302998
\(367\) 28.8148 1.50412 0.752059 0.659095i \(-0.229061\pi\)
0.752059 + 0.659095i \(0.229061\pi\)
\(368\) −51.9407 −2.70760
\(369\) −34.0926 −1.77479
\(370\) −1.30257 −0.0677174
\(371\) −12.8688 −0.668115
\(372\) −0.294127 −0.0152498
\(373\) 20.6301 1.06818 0.534092 0.845426i \(-0.320653\pi\)
0.534092 + 0.845426i \(0.320653\pi\)
\(374\) −16.4498 −0.850599
\(375\) −0.179292 −0.00925859
\(376\) 75.7740 3.90774
\(377\) 42.6592 2.19706
\(378\) −5.78691 −0.297647
\(379\) −1.14856 −0.0589978 −0.0294989 0.999565i \(-0.509391\pi\)
−0.0294989 + 0.999565i \(0.509391\pi\)
\(380\) −19.3523 −0.992753
\(381\) 0.00109419 5.60572e−5 0
\(382\) −17.1042 −0.875126
\(383\) −5.38815 −0.275322 −0.137661 0.990479i \(-0.543958\pi\)
−0.137661 + 0.990479i \(0.543958\pi\)
\(384\) −0.998147 −0.0509365
\(385\) 2.09214 0.106625
\(386\) −13.5111 −0.687699
\(387\) 9.97139 0.506874
\(388\) 12.0053 0.609477
\(389\) −0.261601 −0.0132637 −0.00663185 0.999978i \(-0.502111\pi\)
−0.00663185 + 0.999978i \(0.502111\pi\)
\(390\) −2.31621 −0.117286
\(391\) −38.5988 −1.95202
\(392\) 18.1909 0.918780
\(393\) −3.04813 −0.153758
\(394\) 4.40707 0.222025
\(395\) 13.0212 0.655165
\(396\) −13.8978 −0.698390
\(397\) −9.96780 −0.500270 −0.250135 0.968211i \(-0.580475\pi\)
−0.250135 + 0.968211i \(0.580475\pi\)
\(398\) 58.3639 2.92552
\(399\) 1.55017 0.0776058
\(400\) 8.56281 0.428140
\(401\) 21.5435 1.07583 0.537917 0.842998i \(-0.319211\pi\)
0.537917 + 0.842998i \(0.319211\pi\)
\(402\) 0.338593 0.0168875
\(403\) −1.75070 −0.0872086
\(404\) 88.1485 4.38555
\(405\) 8.71172 0.432889
\(406\) 46.1681 2.29128
\(407\) 0.503875 0.0249761
\(408\) 7.91233 0.391719
\(409\) −4.12783 −0.204108 −0.102054 0.994779i \(-0.532541\pi\)
−0.102054 + 0.994779i \(0.532541\pi\)
\(410\) −29.6958 −1.46657
\(411\) 0.548344 0.0270478
\(412\) −25.1703 −1.24005
\(413\) 22.8087 1.12234
\(414\) −46.5385 −2.28724
\(415\) −2.88990 −0.141860
\(416\) 41.3044 2.02512
\(417\) −2.31332 −0.113284
\(418\) 10.6834 0.522541
\(419\) −27.0062 −1.31934 −0.659669 0.751556i \(-0.729303\pi\)
−0.659669 + 0.751556i \(0.729303\pi\)
\(420\) −1.75652 −0.0857095
\(421\) 0.901224 0.0439230 0.0219615 0.999759i \(-0.493009\pi\)
0.0219615 + 0.999759i \(0.493009\pi\)
\(422\) −20.5820 −1.00191
\(423\) 32.4265 1.57663
\(424\) 42.6589 2.07170
\(425\) 6.36330 0.308665
\(426\) 4.29912 0.208293
\(427\) 26.1657 1.26625
\(428\) 51.5955 2.49396
\(429\) 0.895983 0.0432585
\(430\) 8.68544 0.418849
\(431\) −13.1919 −0.635432 −0.317716 0.948186i \(-0.602916\pi\)
−0.317716 + 0.948186i \(0.602916\pi\)
\(432\) 9.16210 0.440812
\(433\) −0.366034 −0.0175905 −0.00879524 0.999961i \(-0.502800\pi\)
−0.00879524 + 0.999961i \(0.502800\pi\)
\(434\) −1.89470 −0.0909485
\(435\) 1.53050 0.0733819
\(436\) −28.3495 −1.35770
\(437\) 25.0681 1.19917
\(438\) 0.463488 0.0221463
\(439\) 4.48337 0.213980 0.106990 0.994260i \(-0.465879\pi\)
0.106990 + 0.994260i \(0.465879\pi\)
\(440\) −6.93525 −0.330625
\(441\) 7.78458 0.370694
\(442\) 82.2053 3.91011
\(443\) −23.2967 −1.10686 −0.553429 0.832896i \(-0.686681\pi\)
−0.553429 + 0.832896i \(0.686681\pi\)
\(444\) −0.423044 −0.0200768
\(445\) 12.2092 0.578773
\(446\) 25.4945 1.20720
\(447\) 3.21085 0.151868
\(448\) 8.87270 0.419196
\(449\) 21.9408 1.03545 0.517724 0.855547i \(-0.326779\pi\)
0.517724 + 0.855547i \(0.326779\pi\)
\(450\) 7.67222 0.361672
\(451\) 11.4873 0.540915
\(452\) 63.0656 2.96635
\(453\) 0.0251557 0.00118192
\(454\) −28.7139 −1.34761
\(455\) −10.4551 −0.490144
\(456\) −5.13869 −0.240641
\(457\) −4.68888 −0.219337 −0.109668 0.993968i \(-0.534979\pi\)
−0.109668 + 0.993968i \(0.534979\pi\)
\(458\) 29.7124 1.38837
\(459\) 6.80864 0.317800
\(460\) −28.4050 −1.32439
\(461\) 4.56239 0.212492 0.106246 0.994340i \(-0.466117\pi\)
0.106246 + 0.994340i \(0.466117\pi\)
\(462\) 0.969681 0.0451136
\(463\) −8.20782 −0.381450 −0.190725 0.981644i \(-0.561084\pi\)
−0.190725 + 0.981644i \(0.561084\pi\)
\(464\) −73.0953 −3.39336
\(465\) −0.0628105 −0.00291277
\(466\) −14.5626 −0.674600
\(467\) 13.6034 0.629492 0.314746 0.949176i \(-0.398081\pi\)
0.314746 + 0.949176i \(0.398081\pi\)
\(468\) 69.4521 3.21042
\(469\) 1.52837 0.0705736
\(470\) 28.2447 1.30283
\(471\) 2.08259 0.0959607
\(472\) −75.6088 −3.48018
\(473\) −3.35980 −0.154484
\(474\) 6.03515 0.277204
\(475\) −4.13266 −0.189620
\(476\) 62.3412 2.85740
\(477\) 18.2554 0.835856
\(478\) 5.84897 0.267526
\(479\) −1.29325 −0.0590901 −0.0295450 0.999563i \(-0.509406\pi\)
−0.0295450 + 0.999563i \(0.509406\pi\)
\(480\) 1.48189 0.0676389
\(481\) −2.51804 −0.114813
\(482\) 3.93091 0.179048
\(483\) 2.27532 0.103530
\(484\) 4.68277 0.212853
\(485\) 2.56372 0.116412
\(486\) 12.3359 0.559566
\(487\) 28.5653 1.29442 0.647209 0.762312i \(-0.275936\pi\)
0.647209 + 0.762312i \(0.275936\pi\)
\(488\) −86.7369 −3.92640
\(489\) −1.70374 −0.0770460
\(490\) 6.78064 0.306318
\(491\) 24.6944 1.11444 0.557221 0.830364i \(-0.311867\pi\)
0.557221 + 0.830364i \(0.311867\pi\)
\(492\) −9.64452 −0.434808
\(493\) −54.3195 −2.44643
\(494\) −53.3885 −2.40206
\(495\) −2.96785 −0.133395
\(496\) 2.99977 0.134694
\(497\) 19.4058 0.870468
\(498\) −1.33944 −0.0600216
\(499\) 14.0234 0.627772 0.313886 0.949461i \(-0.398369\pi\)
0.313886 + 0.949461i \(0.398369\pi\)
\(500\) 4.68277 0.209420
\(501\) 1.30405 0.0582605
\(502\) 46.0055 2.05333
\(503\) −11.2115 −0.499896 −0.249948 0.968259i \(-0.580414\pi\)
−0.249948 + 0.968259i \(0.580414\pi\)
\(504\) 43.0621 1.91814
\(505\) 18.8240 0.837657
\(506\) 15.6809 0.697099
\(507\) −2.14675 −0.0953404
\(508\) −0.0285783 −0.00126796
\(509\) −27.9960 −1.24090 −0.620451 0.784245i \(-0.713051\pi\)
−0.620451 + 0.784245i \(0.713051\pi\)
\(510\) 2.94931 0.130598
\(511\) 2.09214 0.0925507
\(512\) 47.9965 2.12117
\(513\) −4.42190 −0.195232
\(514\) −31.0594 −1.36997
\(515\) −5.37508 −0.236854
\(516\) 2.82083 0.124180
\(517\) −10.9259 −0.480521
\(518\) −2.72515 −0.119736
\(519\) −2.53418 −0.111238
\(520\) 34.6579 1.51985
\(521\) −33.4094 −1.46369 −0.731846 0.681471i \(-0.761341\pi\)
−0.731846 + 0.681471i \(0.761341\pi\)
\(522\) −65.4929 −2.86655
\(523\) 7.85907 0.343653 0.171826 0.985127i \(-0.445033\pi\)
0.171826 + 0.985127i \(0.445033\pi\)
\(524\) 79.6117 3.47785
\(525\) −0.375103 −0.0163708
\(526\) −27.1133 −1.18220
\(527\) 2.22923 0.0971067
\(528\) −1.53524 −0.0668128
\(529\) 13.7945 0.599761
\(530\) 15.9011 0.690698
\(531\) −32.3558 −1.40412
\(532\) −40.4877 −1.75536
\(533\) −57.4059 −2.48653
\(534\) 5.65883 0.244882
\(535\) 11.0181 0.476356
\(536\) −5.06642 −0.218836
\(537\) −3.34581 −0.144382
\(538\) −15.0008 −0.646730
\(539\) −2.62296 −0.112979
\(540\) 5.01051 0.215618
\(541\) 22.9379 0.986179 0.493090 0.869978i \(-0.335867\pi\)
0.493090 + 0.869978i \(0.335867\pi\)
\(542\) 34.1292 1.46598
\(543\) 3.64632 0.156479
\(544\) −52.5944 −2.25496
\(545\) −6.05401 −0.259325
\(546\) −4.84583 −0.207382
\(547\) −21.6771 −0.926848 −0.463424 0.886137i \(-0.653379\pi\)
−0.463424 + 0.886137i \(0.653379\pi\)
\(548\) −14.3217 −0.611794
\(549\) −37.1180 −1.58416
\(550\) −2.58511 −0.110229
\(551\) 35.2780 1.50289
\(552\) −7.54247 −0.321029
\(553\) 27.2420 1.15845
\(554\) 71.6444 3.04388
\(555\) −0.0903406 −0.00383474
\(556\) 60.4197 2.56237
\(557\) −34.3352 −1.45483 −0.727414 0.686199i \(-0.759278\pi\)
−0.727414 + 0.686199i \(0.759278\pi\)
\(558\) 2.68778 0.113783
\(559\) 16.7901 0.710145
\(560\) 17.9146 0.757029
\(561\) −1.14089 −0.0481683
\(562\) −68.1789 −2.87595
\(563\) −6.73012 −0.283641 −0.141820 0.989892i \(-0.545296\pi\)
−0.141820 + 0.989892i \(0.545296\pi\)
\(564\) 9.17321 0.386262
\(565\) 13.4676 0.566585
\(566\) 9.23687 0.388255
\(567\) 18.2261 0.765425
\(568\) −64.3284 −2.69916
\(569\) 12.9829 0.544270 0.272135 0.962259i \(-0.412270\pi\)
0.272135 + 0.962259i \(0.412270\pi\)
\(570\) −1.91544 −0.0802290
\(571\) 25.7028 1.07563 0.537815 0.843063i \(-0.319250\pi\)
0.537815 + 0.843063i \(0.319250\pi\)
\(572\) −23.4014 −0.978463
\(573\) −1.18627 −0.0495572
\(574\) −62.1277 −2.59316
\(575\) −6.06585 −0.252963
\(576\) −12.5866 −0.524442
\(577\) −10.6899 −0.445026 −0.222513 0.974930i \(-0.571426\pi\)
−0.222513 + 0.974930i \(0.571426\pi\)
\(578\) −60.7281 −2.52596
\(579\) −0.937074 −0.0389435
\(580\) −39.9739 −1.65982
\(581\) −6.04608 −0.250834
\(582\) 1.18825 0.0492547
\(583\) −6.15103 −0.254750
\(584\) −6.93525 −0.286983
\(585\) 14.8314 0.613203
\(586\) −13.8225 −0.571004
\(587\) −9.65922 −0.398679 −0.199339 0.979931i \(-0.563880\pi\)
−0.199339 + 0.979931i \(0.563880\pi\)
\(588\) 2.20219 0.0908170
\(589\) −1.44778 −0.0596547
\(590\) −28.1831 −1.16028
\(591\) 0.305655 0.0125730
\(592\) 4.31458 0.177328
\(593\) −11.0147 −0.452320 −0.226160 0.974090i \(-0.572617\pi\)
−0.226160 + 0.974090i \(0.572617\pi\)
\(594\) −2.76603 −0.113492
\(595\) 13.3129 0.545775
\(596\) −83.8615 −3.43510
\(597\) 4.04787 0.165668
\(598\) −78.3627 −3.20449
\(599\) 28.2804 1.15550 0.577752 0.816212i \(-0.303930\pi\)
0.577752 + 0.816212i \(0.303930\pi\)
\(600\) 1.24343 0.0507629
\(601\) 37.9620 1.54850 0.774251 0.632878i \(-0.218127\pi\)
0.774251 + 0.632878i \(0.218127\pi\)
\(602\) 18.1711 0.740599
\(603\) −2.16811 −0.0882923
\(604\) −0.657021 −0.0267338
\(605\) 1.00000 0.0406558
\(606\) 8.72471 0.354417
\(607\) 10.8604 0.440810 0.220405 0.975408i \(-0.429262\pi\)
0.220405 + 0.975408i \(0.429262\pi\)
\(608\) 34.1576 1.38527
\(609\) 3.20202 0.129752
\(610\) −32.3311 −1.30905
\(611\) 54.6006 2.20890
\(612\) −88.4357 −3.57480
\(613\) 31.8532 1.28654 0.643269 0.765640i \(-0.277578\pi\)
0.643269 + 0.765640i \(0.277578\pi\)
\(614\) −8.99266 −0.362914
\(615\) −2.05957 −0.0830501
\(616\) −14.5095 −0.584604
\(617\) 36.5701 1.47226 0.736128 0.676842i \(-0.236652\pi\)
0.736128 + 0.676842i \(0.236652\pi\)
\(618\) −2.49129 −0.100214
\(619\) 18.9817 0.762938 0.381469 0.924382i \(-0.375418\pi\)
0.381469 + 0.924382i \(0.375418\pi\)
\(620\) 1.64050 0.0658839
\(621\) −6.49038 −0.260450
\(622\) −41.3002 −1.65599
\(623\) 25.5434 1.02337
\(624\) 7.67213 0.307131
\(625\) 1.00000 0.0400000
\(626\) −67.5717 −2.70071
\(627\) 0.740953 0.0295908
\(628\) −54.3934 −2.17053
\(629\) 3.20630 0.127844
\(630\) 16.0513 0.639500
\(631\) −7.09028 −0.282260 −0.141130 0.989991i \(-0.545074\pi\)
−0.141130 + 0.989991i \(0.545074\pi\)
\(632\) −90.3050 −3.59214
\(633\) −1.42748 −0.0567371
\(634\) −20.8696 −0.828838
\(635\) −0.00610286 −0.000242185 0
\(636\) 5.16430 0.204778
\(637\) 13.1079 0.519353
\(638\) 22.0674 0.873658
\(639\) −27.5286 −1.08901
\(640\) 5.56716 0.220061
\(641\) 8.41090 0.332211 0.166105 0.986108i \(-0.446881\pi\)
0.166105 + 0.986108i \(0.446881\pi\)
\(642\) 5.10678 0.201549
\(643\) 43.0220 1.69662 0.848311 0.529499i \(-0.177620\pi\)
0.848311 + 0.529499i \(0.177620\pi\)
\(644\) −59.4271 −2.34176
\(645\) 0.602384 0.0237189
\(646\) 67.9815 2.67470
\(647\) −30.4454 −1.19693 −0.598466 0.801148i \(-0.704223\pi\)
−0.598466 + 0.801148i \(0.704223\pi\)
\(648\) −60.4180 −2.37344
\(649\) 10.9021 0.427945
\(650\) 12.9187 0.506712
\(651\) −0.131408 −0.00515030
\(652\) 44.4987 1.74270
\(653\) −38.8776 −1.52140 −0.760700 0.649104i \(-0.775144\pi\)
−0.760700 + 0.649104i \(0.775144\pi\)
\(654\) −2.80596 −0.109722
\(655\) 17.0010 0.664283
\(656\) 98.3634 3.84045
\(657\) −2.96785 −0.115787
\(658\) 59.0917 2.30363
\(659\) 11.3235 0.441100 0.220550 0.975376i \(-0.429215\pi\)
0.220550 + 0.975376i \(0.429215\pi\)
\(660\) −0.839582 −0.0326807
\(661\) −0.189124 −0.00735607 −0.00367803 0.999993i \(-0.501171\pi\)
−0.00367803 + 0.999993i \(0.501171\pi\)
\(662\) 71.2313 2.76848
\(663\) 5.70141 0.221424
\(664\) 20.0422 0.777789
\(665\) −8.64610 −0.335281
\(666\) 3.86584 0.149798
\(667\) 51.7803 2.00494
\(668\) −34.0593 −1.31779
\(669\) 1.76819 0.0683622
\(670\) −1.88850 −0.0729591
\(671\) 12.5067 0.482815
\(672\) 3.10033 0.119598
\(673\) 38.9986 1.50328 0.751642 0.659571i \(-0.229262\pi\)
0.751642 + 0.659571i \(0.229262\pi\)
\(674\) −42.5907 −1.64053
\(675\) 1.06999 0.0411838
\(676\) 56.0691 2.15650
\(677\) −44.1618 −1.69728 −0.848638 0.528975i \(-0.822577\pi\)
−0.848638 + 0.528975i \(0.822577\pi\)
\(678\) 6.24206 0.239725
\(679\) 5.36365 0.205838
\(680\) −44.1310 −1.69235
\(681\) −1.99147 −0.0763134
\(682\) −0.905630 −0.0346783
\(683\) 6.81871 0.260911 0.130455 0.991454i \(-0.458356\pi\)
0.130455 + 0.991454i \(0.458356\pi\)
\(684\) 57.4349 2.19608
\(685\) −3.05839 −0.116855
\(686\) 52.0448 1.98708
\(687\) 2.06072 0.0786215
\(688\) −28.7693 −1.09682
\(689\) 30.7388 1.17106
\(690\) −2.81145 −0.107030
\(691\) 26.8674 1.02208 0.511042 0.859556i \(-0.329260\pi\)
0.511042 + 0.859556i \(0.329260\pi\)
\(692\) 66.1881 2.51609
\(693\) −6.20916 −0.235866
\(694\) −32.4095 −1.23025
\(695\) 12.9025 0.489422
\(696\) −10.6144 −0.402338
\(697\) 73.0970 2.76874
\(698\) 22.9560 0.868897
\(699\) −1.01000 −0.0382017
\(700\) 9.79700 0.370292
\(701\) −6.55924 −0.247739 −0.123870 0.992299i \(-0.539530\pi\)
−0.123870 + 0.992299i \(0.539530\pi\)
\(702\) 13.8228 0.521709
\(703\) −2.08235 −0.0785371
\(704\) 4.24098 0.159838
\(705\) 1.95893 0.0737775
\(706\) 19.4051 0.730320
\(707\) 39.3824 1.48113
\(708\) −9.15321 −0.343999
\(709\) 19.8773 0.746509 0.373254 0.927729i \(-0.378242\pi\)
0.373254 + 0.927729i \(0.378242\pi\)
\(710\) −23.9784 −0.899891
\(711\) −38.6449 −1.44930
\(712\) −84.6740 −3.17329
\(713\) −2.12502 −0.0795828
\(714\) 6.17036 0.230920
\(715\) −4.99735 −0.186890
\(716\) 87.3865 3.26579
\(717\) 0.405659 0.0151496
\(718\) −82.7165 −3.08695
\(719\) 1.86277 0.0694694 0.0347347 0.999397i \(-0.488941\pi\)
0.0347347 + 0.999397i \(0.488941\pi\)
\(720\) −25.4132 −0.947093
\(721\) −11.2454 −0.418801
\(722\) 4.96621 0.184823
\(723\) 0.272631 0.0101392
\(724\) −95.2352 −3.53939
\(725\) −8.53637 −0.317033
\(726\) 0.463488 0.0172017
\(727\) −15.5780 −0.577755 −0.288877 0.957366i \(-0.593282\pi\)
−0.288877 + 0.957366i \(0.593282\pi\)
\(728\) 72.5090 2.68736
\(729\) −25.2796 −0.936282
\(730\) −2.58511 −0.0956791
\(731\) −21.3794 −0.790745
\(732\) −10.5004 −0.388105
\(733\) 40.3439 1.49014 0.745068 0.666989i \(-0.232417\pi\)
0.745068 + 0.666989i \(0.232417\pi\)
\(734\) −74.4892 −2.74945
\(735\) 0.470276 0.0173464
\(736\) 50.1359 1.84803
\(737\) 0.730531 0.0269095
\(738\) 88.1329 3.24422
\(739\) 44.3015 1.62966 0.814829 0.579701i \(-0.196831\pi\)
0.814829 + 0.579701i \(0.196831\pi\)
\(740\) 2.35953 0.0867381
\(741\) −3.70280 −0.136026
\(742\) 33.2672 1.22128
\(743\) −17.4037 −0.638480 −0.319240 0.947674i \(-0.603428\pi\)
−0.319240 + 0.947674i \(0.603428\pi\)
\(744\) 0.435607 0.0159701
\(745\) −17.9085 −0.656117
\(746\) −53.3309 −1.95258
\(747\) 8.57682 0.313809
\(748\) 29.7979 1.08952
\(749\) 23.0515 0.842282
\(750\) 0.463488 0.0169242
\(751\) 30.7370 1.12161 0.560804 0.827949i \(-0.310492\pi\)
0.560804 + 0.827949i \(0.310492\pi\)
\(752\) −93.5566 −3.41166
\(753\) 3.19074 0.116277
\(754\) −110.279 −4.01611
\(755\) −0.140306 −0.00510626
\(756\) 10.4827 0.381251
\(757\) −18.3644 −0.667466 −0.333733 0.942668i \(-0.608308\pi\)
−0.333733 + 0.942668i \(0.608308\pi\)
\(758\) 2.96916 0.107845
\(759\) 1.08756 0.0394758
\(760\) 28.6611 1.03965
\(761\) 0.638564 0.0231479 0.0115740 0.999933i \(-0.496316\pi\)
0.0115740 + 0.999933i \(0.496316\pi\)
\(762\) −0.00282860 −0.000102470 0
\(763\) −12.6658 −0.458533
\(764\) 30.9833 1.12093
\(765\) −18.8853 −0.682801
\(766\) 13.9289 0.503273
\(767\) −54.4816 −1.96722
\(768\) 4.10106 0.147984
\(769\) 22.1001 0.796949 0.398474 0.917179i \(-0.369540\pi\)
0.398474 + 0.917179i \(0.369540\pi\)
\(770\) −5.40839 −0.194905
\(771\) −2.15414 −0.0775796
\(772\) 24.4746 0.880862
\(773\) 50.3966 1.81264 0.906320 0.422591i \(-0.138879\pi\)
0.906320 + 0.422591i \(0.138879\pi\)
\(774\) −25.7771 −0.926539
\(775\) 0.350326 0.0125841
\(776\) −17.7800 −0.638266
\(777\) −0.189005 −0.00678051
\(778\) 0.676266 0.0242453
\(779\) −47.4731 −1.70090
\(780\) 4.19569 0.150230
\(781\) 9.27558 0.331906
\(782\) 99.7819 3.56819
\(783\) −9.13381 −0.326416
\(784\) −22.4599 −0.802141
\(785\) −11.6156 −0.414580
\(786\) 7.87975 0.281061
\(787\) −37.6568 −1.34232 −0.671161 0.741312i \(-0.734204\pi\)
−0.671161 + 0.741312i \(0.734204\pi\)
\(788\) −7.98316 −0.284388
\(789\) −1.88046 −0.0669462
\(790\) −33.6611 −1.19761
\(791\) 28.1760 1.00182
\(792\) 20.5828 0.731378
\(793\) −62.5002 −2.21945
\(794\) 25.7678 0.914466
\(795\) 1.10283 0.0391133
\(796\) −105.723 −3.74725
\(797\) −40.5494 −1.43633 −0.718167 0.695871i \(-0.755019\pi\)
−0.718167 + 0.695871i \(0.755019\pi\)
\(798\) −4.00736 −0.141859
\(799\) −69.5248 −2.45961
\(800\) −8.26527 −0.292221
\(801\) −36.2352 −1.28031
\(802\) −55.6924 −1.96657
\(803\) 1.00000 0.0352892
\(804\) −0.613341 −0.0216309
\(805\) −12.6906 −0.447284
\(806\) 4.52575 0.159413
\(807\) −1.04039 −0.0366235
\(808\) −130.549 −4.59270
\(809\) −4.91724 −0.172881 −0.0864405 0.996257i \(-0.527549\pi\)
−0.0864405 + 0.996257i \(0.527549\pi\)
\(810\) −22.5207 −0.791298
\(811\) −47.5932 −1.67122 −0.835612 0.549320i \(-0.814887\pi\)
−0.835612 + 0.549320i \(0.814887\pi\)
\(812\) −83.6308 −2.93487
\(813\) 2.36706 0.0830163
\(814\) −1.30257 −0.0456550
\(815\) 9.50264 0.332863
\(816\) −9.76919 −0.341990
\(817\) 13.8849 0.485772
\(818\) 10.6709 0.373099
\(819\) 31.0293 1.08425
\(820\) 53.7923 1.87851
\(821\) 17.7401 0.619132 0.309566 0.950878i \(-0.399816\pi\)
0.309566 + 0.950878i \(0.399816\pi\)
\(822\) −1.41753 −0.0494419
\(823\) 1.08036 0.0376591 0.0188296 0.999823i \(-0.494006\pi\)
0.0188296 + 0.999823i \(0.494006\pi\)
\(824\) 37.2775 1.29862
\(825\) −0.179292 −0.00624214
\(826\) −58.9628 −2.05158
\(827\) −41.4352 −1.44084 −0.720422 0.693536i \(-0.756052\pi\)
−0.720422 + 0.693536i \(0.756052\pi\)
\(828\) 84.3018 2.92969
\(829\) 49.9878 1.73615 0.868074 0.496435i \(-0.165358\pi\)
0.868074 + 0.496435i \(0.165358\pi\)
\(830\) 7.47071 0.259312
\(831\) 4.96894 0.172371
\(832\) −21.1936 −0.734757
\(833\) −16.6907 −0.578298
\(834\) 5.98018 0.207077
\(835\) −7.27332 −0.251704
\(836\) −19.3523 −0.669314
\(837\) 0.374844 0.0129565
\(838\) 69.8138 2.41168
\(839\) −51.9410 −1.79320 −0.896602 0.442837i \(-0.853972\pi\)
−0.896602 + 0.442837i \(0.853972\pi\)
\(840\) 2.60143 0.0897579
\(841\) 43.8696 1.51275
\(842\) −2.32976 −0.0802888
\(843\) −4.72859 −0.162861
\(844\) 37.2831 1.28334
\(845\) 11.9735 0.411901
\(846\) −83.8260 −2.88200
\(847\) 2.09214 0.0718867
\(848\) −52.6701 −1.80870
\(849\) 0.640630 0.0219863
\(850\) −16.4498 −0.564223
\(851\) −3.05643 −0.104773
\(852\) −7.78761 −0.266799
\(853\) −35.1271 −1.20273 −0.601365 0.798974i \(-0.705376\pi\)
−0.601365 + 0.798974i \(0.705376\pi\)
\(854\) −67.6410 −2.31463
\(855\) 12.2651 0.419459
\(856\) −76.4136 −2.61176
\(857\) −7.27774 −0.248603 −0.124301 0.992244i \(-0.539669\pi\)
−0.124301 + 0.992244i \(0.539669\pi\)
\(858\) −2.31621 −0.0790742
\(859\) −43.2845 −1.47685 −0.738425 0.674336i \(-0.764430\pi\)
−0.738425 + 0.674336i \(0.764430\pi\)
\(860\) −15.7332 −0.536497
\(861\) −4.30891 −0.146847
\(862\) 34.1025 1.16154
\(863\) 47.4135 1.61397 0.806987 0.590570i \(-0.201097\pi\)
0.806987 + 0.590570i \(0.201097\pi\)
\(864\) −8.84373 −0.300870
\(865\) 14.1344 0.480583
\(866\) 0.946237 0.0321544
\(867\) −4.21184 −0.143042
\(868\) 3.43214 0.116495
\(869\) 13.0212 0.441712
\(870\) −3.95651 −0.134138
\(871\) −3.65072 −0.123700
\(872\) 41.9860 1.42183
\(873\) −7.60875 −0.257517
\(874\) −64.8037 −2.19202
\(875\) 2.09214 0.0707271
\(876\) −0.839582 −0.0283669
\(877\) 36.3976 1.22906 0.614529 0.788894i \(-0.289346\pi\)
0.614529 + 0.788894i \(0.289346\pi\)
\(878\) −11.5900 −0.391143
\(879\) −0.958672 −0.0323352
\(880\) 8.56281 0.288652
\(881\) −34.3913 −1.15867 −0.579336 0.815089i \(-0.696688\pi\)
−0.579336 + 0.815089i \(0.696688\pi\)
\(882\) −20.1240 −0.677609
\(883\) −16.5031 −0.555373 −0.277686 0.960672i \(-0.589568\pi\)
−0.277686 + 0.960672i \(0.589568\pi\)
\(884\) −148.910 −5.00840
\(885\) −1.95466 −0.0657050
\(886\) 60.2244 2.02328
\(887\) −10.5975 −0.355830 −0.177915 0.984046i \(-0.556935\pi\)
−0.177915 + 0.984046i \(0.556935\pi\)
\(888\) 0.626534 0.0210251
\(889\) −0.0127680 −0.000428226 0
\(890\) −31.5621 −1.05797
\(891\) 8.71172 0.291854
\(892\) −46.1819 −1.54629
\(893\) 45.1532 1.51099
\(894\) −8.30039 −0.277606
\(895\) 18.6613 0.623777
\(896\) 11.6473 0.389108
\(897\) −5.43490 −0.181466
\(898\) −56.7192 −1.89274
\(899\) −2.99051 −0.0997392
\(900\) −13.8978 −0.463260
\(901\) −39.1408 −1.30397
\(902\) −29.6958 −0.988763
\(903\) 1.26027 0.0419392
\(904\) −93.4010 −3.10647
\(905\) −20.3374 −0.676037
\(906\) −0.0650302 −0.00216048
\(907\) −39.3670 −1.30716 −0.653581 0.756857i \(-0.726734\pi\)
−0.653581 + 0.756857i \(0.726734\pi\)
\(908\) 52.0136 1.72613
\(909\) −55.8669 −1.85299
\(910\) 27.0276 0.895957
\(911\) −21.8867 −0.725140 −0.362570 0.931957i \(-0.618101\pi\)
−0.362570 + 0.931957i \(0.618101\pi\)
\(912\) 6.34464 0.210092
\(913\) −2.88990 −0.0956419
\(914\) 12.1213 0.400936
\(915\) −2.24234 −0.0741296
\(916\) −53.8223 −1.77834
\(917\) 35.5684 1.17457
\(918\) −17.6011 −0.580922
\(919\) −41.2236 −1.35984 −0.679920 0.733287i \(-0.737985\pi\)
−0.679920 + 0.733287i \(0.737985\pi\)
\(920\) 42.0682 1.38695
\(921\) −0.623692 −0.0205513
\(922\) −11.7943 −0.388423
\(923\) −46.3533 −1.52574
\(924\) −1.75652 −0.0577853
\(925\) 0.503875 0.0165673
\(926\) 21.2181 0.697269
\(927\) 15.9525 0.523947
\(928\) 70.5554 2.31609
\(929\) −24.9756 −0.819424 −0.409712 0.912215i \(-0.634371\pi\)
−0.409712 + 0.912215i \(0.634371\pi\)
\(930\) 0.162372 0.00532438
\(931\) 10.8398 0.355261
\(932\) 26.3793 0.864084
\(933\) −2.86440 −0.0937764
\(934\) −35.1663 −1.15068
\(935\) 6.36330 0.208102
\(936\) −102.859 −3.36207
\(937\) −25.7485 −0.841166 −0.420583 0.907254i \(-0.638174\pi\)
−0.420583 + 0.907254i \(0.638174\pi\)
\(938\) −3.95100 −0.129005
\(939\) −4.68648 −0.152938
\(940\) −51.1636 −1.66877
\(941\) −43.8309 −1.42885 −0.714423 0.699714i \(-0.753311\pi\)
−0.714423 + 0.699714i \(0.753311\pi\)
\(942\) −5.38372 −0.175411
\(943\) −69.6801 −2.26910
\(944\) 93.3526 3.03837
\(945\) 2.23856 0.0728203
\(946\) 8.68544 0.282388
\(947\) −33.9831 −1.10430 −0.552151 0.833744i \(-0.686193\pi\)
−0.552151 + 0.833744i \(0.686193\pi\)
\(948\) −10.9323 −0.355066
\(949\) −4.99735 −0.162221
\(950\) 10.6834 0.346614
\(951\) −1.44743 −0.0469360
\(952\) −92.3282 −2.99237
\(953\) 40.3866 1.30825 0.654125 0.756386i \(-0.273037\pi\)
0.654125 + 0.756386i \(0.273037\pi\)
\(954\) −47.1920 −1.52790
\(955\) 6.61643 0.214103
\(956\) −10.5951 −0.342669
\(957\) 1.53050 0.0494741
\(958\) 3.34319 0.108013
\(959\) −6.39857 −0.206620
\(960\) −0.760372 −0.0245409
\(961\) −30.8773 −0.996041
\(962\) 6.50939 0.209871
\(963\) −32.7003 −1.05375
\(964\) −7.12062 −0.229340
\(965\) 5.22653 0.168248
\(966\) −5.88193 −0.189248
\(967\) 48.5341 1.56075 0.780375 0.625312i \(-0.215028\pi\)
0.780375 + 0.625312i \(0.215028\pi\)
\(968\) −6.93525 −0.222907
\(969\) 4.71490 0.151464
\(970\) −6.62749 −0.212796
\(971\) 22.5799 0.724622 0.362311 0.932057i \(-0.381988\pi\)
0.362311 + 0.932057i \(0.381988\pi\)
\(972\) −22.3457 −0.716740
\(973\) 26.9939 0.865385
\(974\) −73.8444 −2.36613
\(975\) 0.895983 0.0286944
\(976\) 107.092 3.42794
\(977\) 15.5469 0.497391 0.248695 0.968582i \(-0.419998\pi\)
0.248695 + 0.968582i \(0.419998\pi\)
\(978\) 4.40436 0.140836
\(979\) 12.2092 0.390209
\(980\) −12.2827 −0.392358
\(981\) 17.9674 0.573655
\(982\) −63.8376 −2.03714
\(983\) 49.0249 1.56365 0.781826 0.623497i \(-0.214289\pi\)
0.781826 + 0.623497i \(0.214289\pi\)
\(984\) 14.2837 0.455347
\(985\) −1.70479 −0.0543192
\(986\) 140.422 4.47193
\(987\) 4.09834 0.130452
\(988\) 96.7103 3.07676
\(989\) 20.3800 0.648047
\(990\) 7.67222 0.243839
\(991\) −22.3033 −0.708487 −0.354243 0.935153i \(-0.615262\pi\)
−0.354243 + 0.935153i \(0.615262\pi\)
\(992\) −2.89554 −0.0919334
\(993\) 4.94030 0.156776
\(994\) −50.1660 −1.59117
\(995\) −22.5770 −0.715739
\(996\) 2.42631 0.0768807
\(997\) 60.7675 1.92452 0.962262 0.272124i \(-0.0877259\pi\)
0.962262 + 0.272124i \(0.0877259\pi\)
\(998\) −36.2519 −1.14753
\(999\) 0.539139 0.0170576
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))